Search Results (2,297)

The a priori procedure (APP) is concerned with determining appropriate sample sizes to ensure that sample statistics to be obtained are likely to be good estimators of corresponding population parameters. Previous researchers have shown how to compute a priori confidence interval means or locations for normal and skew-normal distributions. However, two critical limitations persist in the literature: (1) While numerous skewed models have been proposed, the APP equations for location parameters have only been formally established for the basic skew-normal distributions. (2) Even within this fundamental framework, the APPs for sample size determinations in estimating locations are constructed on samples of specifically dependent observations having multivariate skew-normal distributions jointly. Our work addresses these limitations by extending a priori reasoning to the more comprehensive unified skew-normal (SUN) distribution. The SUN family not only encompasses multiple existing skew-normal models as special cases but also enables broader practical applications through its capacity to model mixed skewness patterns and diverse tail behaviors. In this paper, we establish APP equations for determining the required sample sizes and set up confidence intervals for the location parameter in the one-sample case, as well as for the difference in locations in matched pairs and two independent samples, assuming independent observations from the SUN family. This extension addresses a critical gap in the literature and offers a valuable contribution to the field. Simulation studies support the equations presented, and two applications involve real data sets for illustrations of our main results. Full article

Icing on eight-bundled conductors can significantly alter their aerodynamic behavior, potentially leading to structural instabilities such as galloping. This study employed wind tunnel experiments and numerical simulations to analyze the aerodynamic parameters of each iced conductor across various angles of attack. The simulations incorporated detailed stranded conductor geometries to assess their influence on aerodynamic accuracy. Incorporating stranded geometry in simulations reduced average errors in lift and drag coefficients by 45–50% compared to smooth models. The Den Hartog coefficient prediction error decreased from 15.6% to 3.9%, indicating improved reliability in oscillation predictions. Additionally, conductors with larger windward areas exhibited more pronounced wake effects, with lower sub-conductors experiencing greater wake interference than upper ones. The above results illustrate that explicit modeling of stranded conductor surfaces enhances the precision of aerodynamic simulations, providing a more accurate framework for predicting icing-induced galloping in multi-bundled conductors. Full article

In engineering design, optimization is crucial for achieving sustainable goals. This involves creating environmentally responsible structures. Optimizing the design is the first step in reducing the environmental impact of construction. Topology optimization (TO) is one way to do this. TO is the process of designing the material layout in the design domain according to selected criteria. The criteria can be explicitly defined to promote sustainability. As a result, a new structure topology is proposed to make the structure both lightweight and durable, with the aim of improving its functionality and reducing its environmental impact. In optimal engineering design, it is particularly important to take into account the structure’s special operating conditions, e.g., loads subject to random changes. Predicting topologies under such conditions is important since random load changes can significantly affect the resulting topologies. In this paper, an easy to implement numerical method for this kind of problem is proposed. The basic idea is to transform a random loads case into the deterministic problem of multiple loads. A heuristic method of Cellular Automata is proposed as a numerical optimization tool. The examples of topology optimization have been performed to illustrate the concept, confirming the efficiency, versatility, and ease of its implementation. Full article

In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims to recover the implied volatility via observable option prices. Using a linearization technique, we rigorously derive a mathematical formulation of the inverse problem in terms of a Fredholm integral equation of the first kind. Based on an integral equation, an efficient numerical reconstruction algorithm is proposed to recover the coefficient. Numerical results for both problems are provided to illustrate the validity and effectiveness of proposed methods. Full article

This study introduces two novel methodologies for solving systems of Fredholm integral equations, with particular emphasis on second-kind equations. The first method integrates the Sinc-collocation technique with a newly developed singular exponential transformation, enhancing convergence behavior and numerical stability. A comprehensive convergence analysis is conducted to support this approach. The second method employs a double exponential transformation, leading to a pair of linear equations whose solvability is established using the double projection method. Rigorous theoretical analysis is presented, including convergence theorems and newly derived error bounds. A system of two Fredholm integral equations is treated as a practical case study. Numerical examples are provided to illustrate the effectiveness and accuracy of the proposed methods, substantiating the theoretical results. Full article

In this study, we focus on solving the nonlinear time-fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations, using the Yang transform iterative method (YTIM). This method combines the Yang transform with a new iterative scheme to construct reliable and efficient solutions. Readers can understand the procedures clearly, since the implementation of Yang transform directly transforms fractional derivative sections into algebraic terms in the given problems. The new iterative scheme is applied to generate series solutions for the provided problems. The fractional derivatives are considered in the Caputo sense. To validate the proposed approach, two numerical examples are analysed and compared with exact solutions, as well as with the results obtained from the fractional reduced differential transform method (FRDTM) and the q-homotopy analysis transform method (q-HATM). The comparisons, presented through both tables and graphical illustrations, confirm the enhanced accuracy and reliability of the proposed method. Moreover, the effect of varying the fractional order is explored, demonstrating convergence of the solution as the order approaches an integer value. Importantly, the time-fractional Hirota–Satsuma coupled KdV and modified Korteweg–de Vries (MKdV) equations investigated in this work are not only of theoretical and computational interest but also possess significant implications for achieving global sustainability goals. Specifically, these equations contribute to the Sustainable Development Goal (SDG) “Life Below Water” by offering advanced modelling capabilities for understanding wave propagation and ocean dynamics, thus supporting marine ecosystem research and management. It is also relevant to SDG “Climate Action” as it aids in the simulation of environmental phenomena crucial to climate change analysis and mitigation. Additionally, the development and application of innovative mathematical modelling techniques align with “Industry, Innovation, and Infrastructure” promoting advanced computational tools for use in ocean engineering, environmental monitoring, and other infrastructure-related domains. Therefore, the proposed method not only advances mathematical and numerical analysis but also fosters interdisciplinary contributions toward sustainable development. Full article

In this work, we consider the problem of minimizing a quasi-convex function over a nonempty closed convex constrained set. In order to approximate a solution of the considered problem, we propose delayed star subgradient methods. The main feature of the proposed methods is that it allows us to use the stale star subgradients when updating the next iteration rather than computing the new star subgradient in every iteration. We subsequently investigate the convergence results of sequences generated by the proposed methods. Finally, we present some numerical experiments on the Cobb–Douglas production efficiency problem to illustrate the effectiveness of the proposed method. Full article

In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of parabolic partial differential equations, thereby validating the proposed spatio-temporal model. Through the implementation of the suggested cross-diffusion mechanism, the model reveals at least one non-constant positive equilibrium state within the susceptible–infected (SI) system. This work demonstrates the potential coexistence of susceptible and infected populations through cross-diffusion and unveils Turing instability within the system. By analyzing codimension-2 Turing–Hopf bifurcation, the study identifies the Turing space within the spatial context. In addition, we explore the results for Turing–Bogdanov–Takens bifurcation. To account for seasonal disease variations, novel perturbations are introduced. Comprehensive numerical simulations illustrate diverse emerging patterns in the Turing space, including holes, strips, and their mixtures. Additionally, the study identifies non-Turing and Turing–Bogdanov–Takens patterns for specific parameter selections. Spatial series and surfaces are graphed to enhance the clarity of the pattern results. This research provides theoretical insights into the implications of cross-diffusion in epidemic modeling, particularly in contexts characterized by localized mobility, clinically evident infections, and community-driven isolation behaviors. Full article

This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing a more accurate description of thermal and mechanical responses in semiconductor materials. The effects of rotation, ramp-type heating, and semiconductor properties on elastic wave propagation are analyzed theoretically. Governing equations are formulated and solved analytically, with numerical simulations illustrating the variations in thermal and elastic wave behavior. The key findings highlight the significant impact of rotation, nonlocal parameters $e_{0}a$, and time derivative fractional order (FO) $\alpha$ on physical quantities, offering insights into the thermoelastic performance of semiconductor nanostructures under dynamic thermal loads. A comparison is made with the previous results to show the impact of the external parameters on the propagation phenomenon. The numerical results show that increasing the rotation rate $\mathsf{\Omega }=5$ causes a phase lag of approximately 22% in thermal and elastic wave peaks. When the thermoelectric coupling parameter ${\mathsf{\epsilon }}_3$ is increased from $-0.8\times {10}^{-42}$ to $1.2\times {10}^{-42}$. The temperature amplitude rises by 17%, while the carrier density peak increases by over 25%. For nonlocal parameter values $\mathsf{\epsilon }=0.3\to 0.6$, high-frequency stress oscillations are damped by more than 35%. The results contribute to the understanding of wave propagation in advanced semiconductor materials, with potential applications in microelectronics, optoelectronics, and nanoscale thermal management. Full article

This paper investigates the existence and uniqueness of bounded nonoscillatory solutions for two classes of m-th-order nonlinear neutral differential equations that incorporate both discrete and distributed delays. By applying Banach’s fixed-point theorem, we establish sufficient conditions under which such solutions exist. The results extend and generalize previous works by relaxing assumptions on the nonlinear terms and accommodating a wider range of feedback structures, including positive, negative, bounded, and unbounded cases. The mathematical framework is unified and applicable to a broad class of problems, providing a comprehensive treatment of neutral equations beyond the first or second order. To demonstrate the practical relevance of the theoretical findings, we analyze a delayed temperature control system as an application and provide numerical simulations to illustrate nonoscillatory behavior. This paper concludes with a discussion of analytical challenges, limitations of the numerical scope, and possible future directions involving stochastic effects and more complex delay structures. Full article

Selective water withdrawals (SWWs) are frequently used to minimize the downstream effects of dams by blending water from different depths to achieve a desired temperature regime in the river. In 2010, an SWW was installed on the outlet structure of the primary hydropower reservoir on the Deschutes River (Oregon, USA) to increase spring temperatures by releasing a combination of surface water and bottom waters from a dam that formerly only had a hypolimnetic outlet. The objective of increasing spring river temperatures was to recreate pre-dam river temperatures and optimize conditions for the spawning and rearing of anadromous fish. The operation of the SWW achieved the target temperature regime, but the release of surface water from a hypereutrophic impoundment resulted in a number of unintended consequences. These changes included significant increases in river pH and dissolved oxygen saturation. Inorganic nitrogen releases decreased in spring but increased in summer. The release of surface water from the reservoir increased levels of plankton in the river resulting in changes to the macroinvertebrates such as increases in filter feeders and a greater percentage of taxa tolerant to reduced water quality. No significant increase in anadromous fish was observed. The presence of large irrigation diversions upstream of the reservoir was not accounted for in the temperature analysis that led to the construction of the SWW. This complicating factor would have reduced flow in the river leading to increased river temperatures at the hydropower site during the measurement period used to develop representations of historical temperature. The analysis supports the use of numerical models to assist in forecast changes associated with SWWs, but the results from this project illustrate the need for greater consideration of complex responses of aquatic communities caused by structural modifications to dams. Full article

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using classical Legendre polynomials is a special case of interpolation with the proposed Legendre Delta-Shaped Basis Functions (LDSBFs). To illustrate the potential of LDSBFs, we apply the corresponding series to approximate a rectangular pulse. The results reveal that Gibbs oscillations decay rapidly, resulting in significantly improved accuracy across smooth regions. This example underscores the effectiveness and novelty of our approach. Furthermore, LDSBFs are employed within the collocation framework to solve Poisson-type equations and systems of nonlinear differential equations arising in energy transfer problems. We also derive new error bounds for interpolation polynomials in a special case, expressed in both the discrete ${(L}_2)$ norm and the Sobolev $\left(H_p\right)$ norm. To validate the proposed method, we compare our results with those obtained using the Legendre pseudospectral method. Numerical experiments confirm that our approach is accurate, efficient, and highly competitive with existing techniques. Full article

The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order $0.5$ subject to a given initial condition. We establish the existence of a unique solution expressed via a Mittag-Leffler-type function. The delta-asymptotic behavior of the solution is examined, and its convergence properties are rigorously analyzed. Numerical experiments are conducted to illustrate the qualitative features of the solution. Furthermore, a neural network-based approximation is employed to validate and compare with the analytical results, confirming the accuracy, stability, and sensitivity of the proposed method. Full article

In the field of intralogistics, new systems are continuously being studied to increase flexibility and adaptability while striving to maintain high handling capabilities and performance. Among these new systems, this article focuses on a novel under-actuated intelligent surface capable of performing various handling tasks with a simplified design and without employing motors. The technology behind the device involves idle rotors, i.e., without motor-driven spinning, whose axis of rotation can be controlled in a few discrete positions. The system’s operation and digital model have already been tested and validated; however, a control system that makes the surface “smart” has not yet been developed. In this context, the following work analyzes control methodologies for the concept. Specifically, in a first phase, a threshold-based method is introduced and tested on a prototype of the surface for sorting and orientation operations. This basic technique involves actuating the surface modules according to pre-assigned rules once a chosen threshold condition is reached. In a second phase, instead, a decentralizd PID control is described and simulated based on real and potential industrial applications. Unlike the first method, in this case, it is the control law that defines the actuation and, through the dynamic description of the device, determines the best combination to achieve the goal. Additionally, the article illustrates how the difficulties introduced by the numerous nonlinearities, due to the under-actuation and the simplifications of the physical system, were overcome. For both control methods, promising results were obtained in terms of handling capability and errors in achieving the desired movement. Full article

Adobe churches are representative of Andean architectural heritage, yet their structural vulnerability to seismic events remains a significant concern. This study evaluates the seismic performance of the 17th-century Church of Santo Tomás de Aquino in Rondocan, Peru, an adobe building that underwent conservation work in the late 1990s. The assessment combines in situ inspections and experimental testing with advanced nonlinear numerical modeling. A finite-element macro-model was developed and calibrated using sonic and ambient vibration tests to replicate the observed structural behavior. Nonlinear static (pushover) analyses were performed in the four principal directions to identify failure mechanisms and to evaluate seismic capacity using the Peruvian seismic code. Kinematic limit analyses were conducted to assess out-of-plane mechanisms using force- and displacement-based criteria. The results revealed critical vulnerabilities in the rear façade and lateral walls, particularly in terms of out-of-plane collapse, while the main façade exhibited a higher capacity but a brittle failure mode. This study illustrates the value of advanced numerical simulations, calibrated with field data, as effective tools for assessing seismic vulnerability in historic adobe buildings. The outcomes highlight the necessity of strengthening measures to balance life safety requirements with preservation goals. Full article